mathematics

[hellotoyou]

OK! Since no one seem to want to answer to this paradox

What about seing it that way?

" There is a barber that shaves those that don't shave themselves."

Does the barber shave himself?

Or, there is a Cretan that once said: All Cretans are liars.

Is this stament true?

Me thinks that Root read Douglas Hofstadters work: Godel, Escher, Bach: An Eternal Golden Braid

[RootDBA]

True..but the paradox originally (in this form) came from Bertrand Russell, although as you show here..it has a long history.

OK..another old one..

which set is the largest (and why):

The set of all integers or the set of all real numbers ?

[Admin1]

I didn't think you could resist joining in on this topic.

Go ahead, you've more than earned the right to post as a member and have a modicum of fun in the bargain.

[Balamut]

earned right.. man you'r talking like 200 years old guru or something.
Do you have feelings?
(no offence, but it looks very strange)

[justin1987]

both, as both of them are infinite.

[RootDBA]

Originally posted by justin1987
both, as both of them are infinite.

Sorry for the delay Justin. Right and wrong

True both are infinite, but there are more real numbers than there are integers.

If you have two sets A= {a1,a2,a3....} and B = {b1,b2,b3...}, then you can say they are the same size if for every element a(n) of A, there is a corresponding member of B, say b(m)- and vice versa. Basicly- that you can pair off each element of each one set with a corresponding member from the other.

However, if you try and do this with the real numbers and the integers, even though both are infinite, you will soon see that there will always be real numbers that have no corresponding match with an integer- hence it must be a larger set.

In fact, the set of integers is know as aleph nul and is the smallest set of infinite size. The set of real numbers is known as aleph one. Now you can do some interesting arithemtic with these concepts (known as transfinite arthemitic) with some rather strange results...but I'll leave that for you to play with

[Imagine]

this stuff is cool...